Strain mapping of LED devices by dark-field inline electron holography: Comparison between deterministic and iterative phase retrieval approaches

Abstract

Dark-field inline electron holography has recently been established as a convenient method to map strain in semiconductor devices, combining high precision, low noise, sub-nm spatial resolution and fields-of-view larger than 1 mu m. Here we compare two approaches to reconstruct the geometric phase from a transmission electron microscopy dark-field focal series and their effects on the strain measurement: the transport-of-intensity-equation (TIE) and a flux-preserving iterative approach. For this task, we used a GaN-based light emitting diode with a highly complex heterostructure as a model system. While the TIE relies on 3 images only but requires the optimization of two free parameters (defocus step and low-limit cut-off frequency), the iterative reconstruction algorithm involves no adjustable parameters and uses images recorded at 9 different planes of focus with quadratically increasing defocus values. Optimum parameters for the TIE-reconstruction could be identified. However, the iterative phase retrieval approach yields the strain values that agree best with the expected strain levels and provides also higher spatial resolution. (c) 2012 Elsevier B.V. All rights reserved.